## Topology & Geometric Group Theory Seminar

## Fall 2007

### 1:30 - 2:30, Malott 253

Tuesday, October 30

**Yvonne
Lai**, UC Davis

*Using simplicial trees to generate an effective compactness theorem
for Coxeter groups
*

Through highly non-constructive methods, works by Bestvina, Culler,
Morgan, Paulin, Rips, Shalen, and Thurston show that if a finitely
presented group does not split over a small subgroup, then the space
of its discrete and faithful actions on **H**^{n}, modulo
conjugation, is compact for all dimensions. We make this result
effective for Coxeter groups. By fixing a presentation and
associating a simplicial tree to a given action, we find that either
the group splits over a small subgroup or there is a constant C and a
point in **H**^{n} that is moved no more than C by any
generator. The constant C depends only on n and the number of
generators in the presentation.

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